Quadric Surfaces (continued)

Hyperbolic Paraboloid

The hyperbolic paraboloid

import numpy as np
import plotly.graph_objects as go

# Generate the grid of x and y values
x = np.linspace(-2, 2, 200)
y = np.linspace(-2, 2, 200)
x, y = np.meshgrid(x, y)

# Define the circular mask
radius = 2
mask = x**2 + y**2 <= radius**2


# Define the hyperbolic paraboloid equation z = (x^2 / a^2) - (y^2 / b^2)
a = 1  # scale factor for x
b = 1  # scale factor for y
z = (x**2 / a**2) - (y**2 / b**2)

# Apply the mask to the z values
z[~mask] = np.nan  # Set values outside the circle to NaN for visualization

# Create the 3D surface plot
fig = go.Figure(data=[go.Surface(z=z, x=x, y=y, colorscale='Viridis', showscale=False)])

# Add titles and labels
fig.update_layout(title='Hyperbolic Paraboloid (Pringle Chip Shape)',
                  scene=dict(
                      xaxis_title='X-axis',
                      yaxis_title='Y-axis',
                      zaxis_title='Z-axis',
                      aspectmode='manual',
                      aspectratio=dict(x=1, y=1, z=0.5)
                  ))

# Show the plot
fig.show()

Alternative method:

# Source: https://dkmj.org/ipython/2415s16/xy-hyperboloid.html
import plotly.offline as py
from plotly.graph_objs import *
import numpy as np
from numpy import pi, cos, sin, exp, log, sqrt
py.init_notebook_mode()

def curve(rfun,tmin=-2,tmax=2,tpts=200,color='black'):
    domain = np.linspace(tmin,tmax,tpts)
    r = [[rfun(t)[i] for t in domain] for i in range(3)]
    trace = Scatter3d(x=r[0],y=r[1],z=r[2],mode='lines',
                      line=Line(color=color,width=3))
    return(trace)

def snake(u,v):
    lu, lv = len(u), len(v)
    path = []

    i, j = 0, 0
    istep, jstep = 1, 1
    while(i < lu):
        while(0 <= j < lv):
            path.append((u[i],v[j]))
            j += jstep
        j -= jstep
        i += istep
        jstep *= -1

    i -= istep
    i -= istep
    istep *= -1
    while(0 <= j < lv):
        while(0 <= i < lu):
            path.append((u[i],v[j]))
            i += istep
        i -= istep
        j += jstep
        istep *= -1
    return path

def surface(rfun,tmin=-2,tmax=2,tpts=20,umin=-2,umax=2,upts=20,color='black'):
    t, u = np.linspace(tmin,tmax,tpts), np.linspace(umin,umax,upts)
    path = snake(t,u)
    r = [[rfun(t,u)[i] for (t,u) in path] for i in range(3)]
    trace = Scatter3d(x=r[0],y=r[1],z=r[2],mode='lines',
                      line=Line(color=color,width=3))
    return(trace)

f = lambda x,y: x*y
xmin=-1
xmax=1
ymin=-1
ymax=1
s = surface(lambda t,u: (t,u,f(t,u)),color='green',tmin=xmin,tmax=xmax,umin=ymin,umax=ymax) #surface z=f(x,y)
py.iplot(Figure(data=Data([s])))

/home/fes33/Documents/Work_-_Web/Worldlines/env/lib/python3.9/site-packages/plotly/graph_objs/_deprecations.py:378: DeprecationWarning:

plotly.graph_objs.Line is deprecated.
Please replace it with one of the following more specific types
  - plotly.graph_objs.scatter.Line
  - plotly.graph_objs.layout.shape.Line
  - etc.


/home/fes33/Documents/Work_-_Web/Worldlines/env/lib/python3.9/site-packages/plotly/graph_objs/_deprecations.py:31: DeprecationWarning:

plotly.graph_objs.Data is deprecated.
Please replace it with a list or tuple of instances of the following types
  - plotly.graph_objs.Scatter
  - plotly.graph_objs.Bar
  - plotly.graph_objs.Area
  - plotly.graph_objs.Histogram
  - etc.